Nature of spin Hall effect in a finite ballistic two-dimensional system with Rashba and Dresselhaus spin-orbit interaction

The spin Hall effect in a finite ballistic two-dimensional system with Rashba and Dresselhaus spin-orbit interaction is studied numerically. We find that the spin Hall conductance is very sensitive to the transverse measuring location, the shape and size of the device, and the strength of the spin-orbit interaction. Not only the amplitude of spin Hall conductance, but also its sign, can change. This nonuniversal behavior of the spin Hall effect is essentially different from that of the charge Hall effect, in which the Hall voltage is almost invariant with the transverse measuring site and is a monotonic function of the strength of the magnetic field. This surprise behavior of the spin Hall conductance is attributed to the fact that the eigenstates of the spin Hall system are extended in the transverse direction and do not form the edge states.